http://www.nysubway.com/airport/newark.html
this link shows you the options to get to manhattan
I have used the PATH / NJ Transit / Airtrain to Newark Airport � Cheapest Method just as it says in the link above found it very easy to get tickets from the machine and get to and from the airport to manhattan, they run regularly
enjoy your trip!
use www.tripadvisor.com or www.virtualtourist.com websites to find things to do unless you just want to see the usual tourist attractions